The statement that linear pairs of angles are always adjacent is true.
What are Linear Pairs?
The pair of angles formed when two lines intersect each other at a point, are called Linear Pairs, the angles formed are adjacent to each other and they share a common arm.
It is asked in the question that linear pairs of angles are always adjacent and the answer is yes, it is a true statement as they have a common arm and an uncommon arm, the sum of the angles is equal to 180 degrees.
Hence, the statement that linear pairs of angles are always adjacent is true.
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y = -2 f(3(x - 4)) - 1 Describe this transformation
The graph y = x^3 is compressed vertically by a factor of 1⁄2 , translated 4 units to the right, and translated 5 units upward.
Write the equation of the transformed function.
The equation of the transformed function is y = 1/2(x - 4)^3 + 5
How to describe the transformation?The parent function is given as:
y = x^3
When the function is vertically compressed by 1/2, the rule is:
(x, y) ⇒ (x, 1/2y)
So, we have
y = 1/2x^3
When translated 4 units right, we have:
y = 1/2(x - 4)^3
When translated 5 units up, we have:
y = 1/2(x - 4)^3 + 5
Hence, the equation of the transformed function is y = 1/2(x - 4)^3 + 5
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When we graph a line using slope and y-intercept, the first point that you graph is
ALWAYS on_____, and you use _____ to get to the next point.
Answer:
y=mx+b is the formula starting with b say it is 4 you put a dot on 4 on the y axis m is 1/2 you go up 1 right 2 on the 4 points then do the same on the next point you get then you get your line. hope this helps
Problem
A prime trio is a collection of three prime numbers [tex]\{p,q,r\}[/tex] in arithemtic progression, with common difference [tex]q-p=r-q[/tex]. For example, the prime trio [tex]\{3,5,7\}[/tex]has common difference 2.
(a) Find a prime trio with common difference 50.
(b) Find two prime trios with common difference 60.
(c) Prove that there is no prime trio with common difference 70.
Answer:
(a) 50:
3 53 103
(b) 60:
7 67 127
11 71 131
Step-by-step explanation:
OK, I think you can prove this with the theorem that any prime greater than 3 is 6n-1 or 6n+1, for integer n. In other words, any prime is near a multiple of 6; it is either one less or one more. The proof for this is very easy, look it up.
Given this fact, if two primes (p,q) are 70 a part, this means the first one has to be a case of 6n+1 and the second one has to be a case of 6n-1. Why? Because the nearest multiple of 6 is 72 and with +1 on one end and -1 on the other end, you can reach a "gap" of 70.
Now for the next two primes (q,r) the same must hold. Only, it can't because this requires q to be both 6n-1 and 6n+1.
A line passes through the point (-2, 8) and has a slope of-5/2.
Write an equation in slope-intercept form for this line.
Answer:
[tex]y = -\frac{5}{2} x + 3[/tex]
Step-by-step explanation:
We are given that a line passes through (-2, 8) and has a slope of -5/2.
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of this line, we can immediately plug it into the equation.
Replace m with -5/2.
[tex]y = -\frac{5}{2} x+ b[/tex]
Now we need to find b.
As the equation passes through the point (-2, 8), we can use its values to help solve for b.
Substitute -2 as x and 8 as y.
[tex]8 = -\frac{5}{2} (-2) +b[/tex]
Multiply.
8 = 5 + b
Subtract 5 from both sides.
3 = b
Replace b with 3 in the equation.
[tex]y = -\frac{5}{2} x + 3[/tex]
Topic: finding the equation of the line (slope-intercept form)
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0. In 1996 Jabu decides to invest in the Stock Exchange. He buys 1200 shares in a company at R6.75 per share. How much did he pay for the shares?
Answer:
[tex]1200\times6.75=R8100[/tex]
Consider a convex hexagon in which all pairs of opposite sides are parallel. Prove that if one pair of opposite sides have equal length, then the other two pairs of opposite sides also have equal length.
A pair of the opposite sides of a hexagon has equal length and this is proved below.
How to illustrate the hexagon?It should be noted that a hexagon is a polygon that has six sides.
In this case, it has 6 sides.
The total angles will be:
= (n - 2) × 180
= (6 - 2) × 180
= 720°
Each angle will hence be:
= 720°/6
= 120°
Each angle are equal and this illustrates that the parallel sides are equal.
A diagram is attached to illustrate the pair of parallel sides.
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6 in.
10 in.
15 in.
V = [?] in.³
area of base
Volume of Prism B.h
Answer:
300
Step-by-step explanation:
A pyramid with a triangle-shaped base whose three triangular faces meet at the ap/ex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid volume formula calculates the base area and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter,, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula:
Volume= 1/3 × Base area × Height
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
3. Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
5. Create a graph of the polynomial function you created in Question 4.
Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
The key features of the function g(x) = (x + 3)(x + 2)(x − 3) are; Maximum Point at g(x) = 6.065; Minimum Point at g(x) = -0.879; 2.593 is the point of inflection
How to identify the features of a Polynomial?1) The Fundamental Theorem of Algebra states that a polynomial of degree "n" has at most "n" number of complex roots.
Since Kelsey argues the function can have as many as three zeros only, then we can say that Kelsey is correct.
2) The g(x) function that I will choose is;
g(x) = (x + 3)(x + 2)(x − 3)
Expanding this gives us;
g(x) = x³ - x² - 4x + 4
To find the key features which are critical points (maximum, minimum, point of Inflection), we will differentiate g(x) with respect to x to get;
g'(x) = 3x² - 2x - 4 = 0
Using quadratic formula gives;
x = 1.535 and Minimum Point; x = -0.869
Thus;
g(1.535) = -0.879 minimum point
g(-0.869) = 6.065 maximum point
Thus;
Maximum Point occurs at g(x) = 6.065
Minimum Point occurs at g(x) = -0.879
g"(x) = 6x -2
At g"(x) = 0, we will have the point of inflection which is at;
x = 1/3
g(1/3) = 2.593 which is the point of inflection
3) The graph of the Polynomial of the function g(x) = (x + 3)(x + 2)(x − 3) is as attached.
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Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = r²h
Write the formula to calculate the height, h.
Answer:
Cone: h = [tex]3\frac{V}{\pi r^{2} }[/tex]
Cylinder: h = [tex]\frac{V}{\pi r^{2} }[/tex]
Step-by-step explanation:
- the formula you described is not the formula for the volume of a cone as it is V = [tex]\pi rx^{2} \frac{h}{3}[/tex]
- to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:
- h = [tex]3\frac{V}{\pi r^{2} }[/tex]
- based on the formula you described, it is closer to a cylinder and the formula for the volume of a cylinder is: V = [tex]\pi r^{2} h[/tex]
- once again, to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:
- h = [tex]\frac{V}{\pi r^{2} }[/tex]
hope this helps :)
Dr. Dominic Estores has written a prescription for a patient to take a preoperative medication at 2200 on the evening before his scheduled surgery. Using the standard time system, what time should you tell the patient to take his medication?
Using the conversion from the 24-hour system to the AM/PM system, the patient should take the medicine at 10 PM.
How to convert from 24 hours to AM/PM?If the hour is between 0 and 11:59, the hour is kept with AM.If the hour is 12, it is PM.If the hour is between 13 and 23:59, the hour the remainder of the division of the hour and 12, PM.22 divided by 12 has remainder 10, hence 22 is equivalent to 10 PM.
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A coach in a train can seat exactly 72 people for a trip. The train has 12 such coaches. If the train made 156 trips in full capacity this year, how many people has it carried in that time. I will give brain to the first person who answers this question correctly.
Answer:
134,784 people
Step-by-step explanation:
Hello!
Let's first find the number of people it can carry on 1 trip. We can do this by multiplying the number of people per coach, by the number of coaches.
72 x 12864The train carries 864 people per trip. We can find the number of people in 156 trips by multiplying 864 by 156.
864 x 156134,784The train, in full capacity, will carry 134,784 people in 156 trips.
Silva the formula I=Prt, in general, to find the principal, p.
Dividing both sides by rt,
[tex]\boxed{P=\frac{I}{rt}}[/tex]
The graph of f(x) was vertically translated down by a value of k to get the function g(x) = 5x + k. What is the value of k?
The value of k in g(x) = 5^x + k is -7
How to determine the value of k?The complete question is added as attachment
The functions are given as:
f(x) = 5^x
g(x) = 5^x + k
From the attached graph, we can see that:
f(x) is shifted down by 7 units to form g(x)
This means that:
g(x)= f(x) - 7
This gives
g(x) = 5^x - 7
Substitute g(x) = 5^x - 7 in g(x) = 5^x + k
5^x + k = 5^x - 7
This gives
k = -7
Hence, the value of k in -7
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The ages of 30 students in a class are given below. Construct a frequency table for grouped data using 6 classes. For convenience, the data has been ordered from smallest to largest. 15, 17, 18, 19, 25, 25, 27, 28, 29, 30, 30, 32, 33, 36, 38, 45, 45, 48, 49, 50, 52, 53, 55, 56, 57, 58, 59, 59, 63, 68 All responses should be whole numbers. Provide your answer below:
Here is the frequency table:
Class Frequency
15 - 24 4
25 - 34 9
35 - 44 2
45 - 54 7
55 - 64 7
65 - 74 1
What is the frequency table?A frequency table is used to track the frequency of a data set. The data ranges from 15 to 68, if the classes are to be 6, then the class interval would have to be 9.
Class Frequency
15 - 24 4
25 - 34 9
35 - 44 2
45 - 54 7
55 - 64 7
65 - 74 1
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You are planning a trip to Bermuda but have heard stories of people getting "lost" in the area that forms what is known as the Bermuda Triangle. You are
curious just how big the area that forms the triangle actually is and decide to investigate. You discover that one side length of the triangle is 900 miles and
another sides is 930 miles and the angle between them is 56 degrees. What is the area that the plane can fly and be in the zone known as the Bermuda
Triangle? Round your answer to the nearest mile.
The area that the plane can fly and be in the zone known as the Bermuda is; 346952 mile²
How to use the area rule to find the area of a triangle?The area rule states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle multiplied by the sine of the angle included by the two sides.
Now, from the question, we are give;
Side 1 = 900 miles
Side 2 = 930 miles
Angle between two sides = 56°.
Thus, by the area rule we have;
Area = (1/2) * 900 * 930 * sin 56°
Area = 346952 mile²
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Please help me....trying to get my HS diploma, i did not graduate :(
Kevin wants to buy an area rug for his living room. He would like the area rug to be no smaller that 48 square feet and no bigger than 80 square feet. If the length is 2 feet more than the width, what are the range of possible values for the length?
Answer:
It would be B.
Step-by-step explanation:
[tex]area = l \times w \\ but \: w = l - 2[/tex]
[tex]area = l(l - 2) = l {}^{2} - 2l[/tex]
[tex]l {}^{2} - 2l \geqslant 48 \\ l {}^{2} - 2l - 48 \geqslant 0 \\ (l + 6)(l - 8) \geqslant 0[/tex]
[tex]l {}^{2} - 2l \leqslant 80 \\ l {}^{2} - 2l - 80 \leqslant 0 \\ (l + 8)(l - 10) \leqslant 0[/tex]
Sol 1: L in ]-∞,-6]U[8,∞[Sol 2: L in [-8,10]Intersection:L belongs [-8,-6[U[8,10]But Length cannot be negativeL belongs [8,10] or 8≤L≤10Describe the transformation of the function, y=1/7 x from y = x.
The transformation of the function, y=1/7 x from y = x is y = 7x
How to determine the transformation?The function is given as:
y = 1/7x
The transformation rule is given as:
y = x
This means that we swap x and y.
So, we have:
x = 1/7 y
Multiply through by 7
y = 7x
Hence, the transformation of the function, y=1/7 x from y = x is y = 7x
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Which expression is equivalent to (2x²y) ³?
O 2x¹y4
2x¹2y3
8x¹ y
O 8x¹2y³
Answer: [tex]8x^6 y^3[/tex]
Step-by-step explanation:
See attached image.
The expression which is equivalent to (2x²y)³ is 8x⁶y³
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (2x²y)³
Two times of x square times of y whole to the power of three
We have to find the equivalent expression of the given expression.
Equivalent expressions are expressions that work the same even though they look different.
We have a property that [tex](a^m)^n=a^m^n[/tex]
So (2x²y)³ = 2³x⁶y³
=8x⁶y³
Hence, the expression which is equivalent to (2x²y)³ is 8x⁶y³
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giving brainliest :)
Answer:
The last one - 256 people
Which of the following is not in the domain of tan(x)? Select all correct answers.
The Domain and Range of tan(x) are mathematically given as
Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]
Range: all Real numbers
What is The Domain and Range of tan(x)?All real numbers are in the domain of the function "y=tan (x)," with the exception of the value "[tex]\pi/2+\pi n[/tex]" for all integers n, which is the case when cos(x) = 0.
It follows that "[tex]\frac{-3 \pi }{2}[/tex]" is not in the domain of "tan (x)" among the possible values.
In conclusion,
Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]
Range: all Real numbers
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20 people show up to the party and robert decides to give them
Answer:
This question looks and sounds like a "personal opinion question" to me.so from my opinion Robert give them a Smack in their ases .
Hope this helps .
Good luck ✅.
The auto parts department of an automotive dealership sends out a mean of 4.2 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3? Round your answer to four decimal places.
The probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.
What are some of the properties of Poisson distribution?The Poisson distribution is a discrete probability distribution that describes the likelihood of a specific number of events occurring in a specified span of time or space, if these events occur at a constant mean rate and regardless of the time since the last occurrence.
Let X ~ Pois(λ)
Then we have:
E(X) = λ = Var(X)
Since standard deviation is the square root (positive) of variance,
Thus,
The standard deviation of X = [tex]\sqrt{\lambda}[/tex]
Its probability function is given by
[tex]f(k; λ) = Pr(X = k) = \dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]
Given the mean is 4.2.
We have to find the probability that on any day, the number of special orders sent out will be exactly 3. Therefore, the value of x will be 5.
Using the Poisson distribution,
[tex]P(x) = \dfrac{e^{-\lambda}\lambda ^x}{x!}\\\\P(5) =\dfrac{e^{-4.2}(4.2)^5}{5!}\\\\P(5) = 0.1633[/tex]
Hence, the probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.
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What is the equation of the function represented by this graph?
Answer:
[tex]\displaystyle g(x) = -(x + 2)(x - 4)[/tex]
Step-by-step explanation:
First, look at the graph to determine whether it opens down or up, which in this case is down, so you insert a negative in front of the expression. Next, locate your x-intercepts [zeros (where the graph insects the x-axis)]. You will see that the graph intersects [tex]\displaystyle [-2, 0][/tex] and [tex]\displaystyle [4, 0],[/tex] so what you do is insert the zeros' OPPOCITES into the equation because according to the vertex equation, [tex]\displaystyle y = A[x - h]^2 + k,[/tex] that negative in front of [tex]\displaystyle h[/tex] gives you the OPPOCITE outcome, so be careful.
I am joyous to assist you at any time.
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your
finding to state whether or not the given r represents a significant linear correlation. Use a significance level of
0.05.
r = 0.543, n = 25
A) Critical values: r = +0.487, no significant linear correlation
B) Critical values: r = +0.396, no significant linear correlation
C) Critical values: r = +0.487, significant linear correlation
D) Critical values: r = +0.396, significant linear correlation
The critical value of r is mathematically given as r = +0.487, with no significant linear correlation. Option A.
What are the critical values of r?
Question Parameters
r = -0.868
n = 5
df = 5 - 2
df = 3
[tex]\alpha / 2 =0.025[/tex]
Critical values [tex]r= \pm 0.878[/tex]
Generally, there exists no linear correlation between the Critical values
as r=0.878
In conclusion, Critical values: r = +0.487, no significant linear correlation
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Find the angle between the vectors A = <2,-3> asnd B = <-2, -5> to the nearest tenth of a degree.
Answer:
55.5
Step-by-step explanation:
answer is 55.491477012331599 which rounded to the nearest tenth is 55.5
when you said to the nearest tenth of degree i assume that meant like rounding to the nearest tenth
Suppose the theoretical probability of winning a prize at a carnival game is 0.18. Based on this probability how many more customers would you have expected to win a prize
Answer:
Could you please provide more context to the problem
Step-by-step explanation:
There is not much context provided for us on this problem, but you can set the decimal to a percentage: 18% of customers win a prize. Now to properly solve this question we need to know either the number of people or the percentage of kids and adults.
The plane 15x − 12y + 20z = 60 is represented by which graph below? Notice the z-axis.
Answer:
b
Step-by-step explanation:
I did it
gym help
when doing any weighted exercises that involve using all or little of my body weight do i count my body weight and the added weight as my “actual weight lifted”? for example i weigh 150lbs and let’s say i did a single rep of weighted overhand chin ups with a single 20lbs weight wrapped around me and i wanted to track how much “actual weight” i just lifted would i write down and track just the 20lbs or my body weight 150lbs plus the weight 20lbs?
You should write down and track only the 20lbs weight during your weighted exercise while ignoring your body weight.
What is actual weight?Actual weight is also referred to as gross weight and it can be defined as the exact (original) weight of an object, as measured using an appropriate weighing scale.
This ultimately implies that, you would write down and track only the 20lbs weight during your weighted exercise such as a single rep of weighted overhand chin ups.
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(a) The coefficient of variation for males is _%
(b) The coefficient of variation for females is _%
(c) Compare the variability of grade point averages of males and females. Choose the correct answer below.
A.
The grade point averages of females and males have the same variation.
B.
The grade point averages of females and males do not vary.
C.
The grade point averages of males are more variable than females.
D.
The grade point averages of females are more variable than males.
The coefficients of variation shows that D. The grade point averages of females are more variable than males.
How to illustrate the information?From the complete information, the coefficients of variation for male is 21.3% and the coefficient of variation for female is 25.1%.
In this case, the coefficients of variation shows that the grade point averages of females are more variable than males.
In conclusion, the correct option is D.
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sari ran for class president. each student in her class voted one time. sari won 25% of the student votes. if sari recived 60 votes, how many students voted altogether
The number of students who voted is 240.
How many students voted?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
The number of students who voted = number of votes Sari received / percentage number
60 / 0.25 = 240
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